Problem 48 Solve the equation. $$-40=-8 x... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 3: Problem 48

Solve the equation. $$-40=-8 x$$

Short Answer

Expert verified

x = 5

Step by step solution

Understand the equation

The given equation is $-40 = -8x$. We need to solve for the variable $x$.

Isolate the variable

To isolate $x$, divide both sides of the equation by $-8$. This is because $x$ is currently being multiplied by $-8$.

Perform the division

Divide $-40$ by $-8$: $-40 / -8 = x $ When you divide -40 by -8, you get 5. This simplifies to $x = 5$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables

When solving equations, one of the key steps is isolating the variable. This means getting the variable alone on one side of the equation. Why is this important? It allows us to see the value of the variable directly. In our example, the equation is $-40 = -8x...$. Our goal is to isolate $x$ so we can determine what it equals. We do this by reversing any operations done to $x$. In this case, $x$ is multiplied by $-8$, so we'll use the opposite operation (division) to reverse it.

Division in Equations

Division is a handy tool in solving equations, especially when a variable is being multiplied by a number. To isolate the variable, we divide both sides of the equation by that number. For example, in the equation $-40 = -8x$, $x$ is multiplied by $-8$. We use division to cancel out this multiplication. Dividing both sides by $-8$ gives us $\frac{-40}{-8}= x$. It is important to perform the same operation on both sides of the equation to maintain equality. After performing the division, we find that $x = 5$.

Solving Linear Equations

Linear equations are the simplest type of equations and they involve variables raised to the power of one. Solving them consists of isolating the variable on one side of the equation, and simplifying the other side. In our step-by-step example, the equation is $-40 = -8x$. We isolated $x$ by dividing both sides by $-8$, and found $ x = 5$. Follow these steps to solve any linear equation:

Identify the equation: Locate the variable you need to solve for.

Isolate the variable: Use operations like addition, subtraction, multiplication, or division to get the variable alone.

Simplify: Perform the necessary operations and simplify your answer.

Understanding these steps will help you solve any linear equation efficiently.

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91影视

Solve the equation. $$-40=-8 x$$

Short Answer

Step by step solution

Understand the equation

Isolate the variable

Perform the division

Key Concepts

Isolating Variables

Division in Equations

Solving Linear Equations

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